Lamina approximations

The stiffness of of a unidirectional lamina in the fiber direction is also given approximately by the rule of mixtures ... 

The fundamental analysis of a laminate can be explained, in principle, by use of a simple two-layered cross-ply laminate (a layer with fibers at 0° to the x-direction on top of an equal-thickness layer with fibers at 90° to the x-direction). We will analyze this laminate approximately by considering what conditions the two unbonded layers in Figure 4-3 must satisfy in order for the two layers to be bonded to form a laminate. Imagine that the layers are separate but are subjected to a load in the x-direction. The force is divided between the two layers such that the x-direction deformation of each layer is identical. That is, the laminae in a laminate must deform alike along the interface between the layers or else fracture must existl Accordingly, deformation compatibility of layers is a requirement for a laminate. Because of the equal x-direction deformation of each layer, the top (0°) layer has the most x-direction ress because it is stiffer than the bottom (90°) layer in the x-direction./ Trie x-direction stresses in the top and bottom layers can be shown to have the relation... 

Composite materials have many distinctive characteristics reiative to isotropic materials that render application of linear elastic fracture mechanics difficult. The anisotropy and heterogeneity, both from the standpoint of the fibers versus the matrix, and from the standpoint of multiple laminae of different orientations, are the principal problems. The extension to homogeneous anisotropic materials should be straightfor-wrard because none of the basic principles used in fracture mechanics is then changed. Thus, the approximation of composite materials by homogeneous anisotropic materials is often made. Then, stress-intensity factors for anisotropic materials are calculated by use of complex variable mapping techniques. 

The sclera is the outer white tough part of the eye, which is an important structural element, with the site of insertion of extraocular muscles. It covers 80% of the exterior surface and is white and nontransparent. It borders the transparent cornea at the pars planar. The sclera is divided into three layers episclera, stroma, and lamina fusca. Only a limited number of blood vessels, originating from arteriolar branches of the anterior ciliary vessels, are found and superficial vessels are mainly confined to the loose outer episclera. Scleral permeability approximates that of the corneal stroma and has been shown to be permeable to solutes up to 70 kDa in molecular weight [14]. 

A dispersion of gas bubbles in a liquid, in which at least one dimension falls within the colloidal size range. Thus a foam typically contains either very small bubble sizes or, more commonly, quite large gas bubbles separated by thin liquid films. The thin liquid films are called lamellae (or laminae ). Sometimes distinctions are drawn as follows. Concentrated foams, in which liquid films are thinner than the bubble sizes and the gas bubbles are polyhedral, are termed polyederschaum . Low-concentration foams, in which the liquid films have thicknesses on the same scale or larger than the bubble sizes and the bubbles are approximately spherical, are termed gas emulsions , gas dispersions , or kugelschaum . See also Evanescent Foam, Froth, Aerated Emulsion. 

Let us focus our attention on a horizontal laminar plane x= x, with v = v. Molecules coming from below and colliding with molecules on this layer may be assumed (in a rough approximation) to have suffered their most recent previous collision on a plane at a distance A below the plane in question. The average momentum component in the shear direction parallel to the lamina (call it the y direction) for one of these molecules is therefore... 

In an electrochemistry-NR experiment, the reflection of neutrons takes place at an interface consisting of five parallel phases as schematically shown in Figure 3.9. Table 3.1 lists the numerical values of the theoretical SLDs of the materials used in typical electrochemical studies. Each phase contributes to the overall measured NR, and to understand the shape of the experimental reflectivity curves it is instructive to examine the contribution of each individual lamina. To do this, a recursion scheme for stratified media described by Parratt [18] can be used to calculate the reflectivity of a simulated interface. These calculated reflectivities are then compared to the reflectivities predicted by the kinematic approximation. Consider a 20 A thick film of a hydrocarbon-based surfactant deposited on a gold/ cliromiurn-modified quartz sample. To simplify the analysis, a mixed D2O/H2O... 

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